## Question

# 1. [Conceptual] Consider a study investigating the association between retail stores' revenue and their marketing budget. The outcome of interest is store's gross revenue

1. [Conceptual] Consider a study investigating the association between retail stores' revenue and their marketing budget. The outcome of interest is store's gross revenue in 2020, yi, for store i = 1,..., n. We further observe each store's allocation of marketing budget across three different marketing strategies: strategy A, strategy B, and strategy C. Let A be the percent of the ith store's marketing budget spent on strategy A, B; be the percent of the ith store's marketing budget spent on strategy B, and C; be the percent of the ith store's marketing budget spent on strategy C. These are the only possible ways to spend the marketing budget, so that Ai + Bi + Ci = 100%. Suppose an analyst fits the following regression model: Yi = A + Bi + 3i + i (1) (a) Why can we not add an intercept to this model? (b) What difficulties arise in interpreting the estimates of the regression coefficients in this model? (c) How else might you interpret the results of this analysis? (For this model, not results of fitting a different model)

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